Evaluation of Explicit Numerical Solution Methods of the Muskingum Model

Abstract

AbstractThe nonlinear Muskingum model is a frequently used hydrologic routing method. In this model, the rate of change of the storage volume with respect to time is expressed by an ordinary first-order differential equation. Generally, this equation has no analytical solution, and thus, should be solved by standard numerical solution methods. Although many optimization techniques have been employed to estimate the parameters for the model, an accurate solution method for calculating the storage time variation of the Muskingum model is still required. Most previous researchers have used an inaccurate explicit Euler’s method along with a manipulated routing equation for calculating the discharge at the downstream end to achieve a better fit for observed data. This manipulation, however, is not acceptable from a mathematical viewpoint. Until now, the storage time variation of the Muskingum model has only been calculated by an explicit Euler’s method; other explicit numerical solution methods have not been u...